Answer to Question #121254 in Geometry for Amya

Question

find the equation of the line, given the following information
Passes through (1,4) and is parallel to y=5x + 2

Answer 1

The given line is,

y = 5x + 2

And the point through which the line parallel to the given line passes is, (1,4).

The slope of y = 5x + 2 is, m = 5.

The line parallel to the given line will also have the same slope.

Using point slope equation of line, we get,

(y - y₁) = 5(x - x₁)

Substituting the point (1,4), we get,

y - 4 = 5(x - 1)

y - 4 = 5x - 5

i.e., y = 5x - 5 + 4

$\therefore$ y = 5x - 1

The line parallel to the line y = 5x + 2 that passes through the point (1,4) is, y = 5x - 1.